Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Experimental and Theoretical Physics

Analytic solutions to the Bloch equations for amplitude- and frequency-modulated fields

Sergey V. Prants, L S Yakupova

Published Apr 1, 1990• 3 citations
OpenAlex

Related papers

Analytic solutions of Bloch equations with phase term for two-pulse photon echo by the phase modulation pulses

Xiurong Ma, Wenzhong Deng, Yunlong Shan

Optoelectronics Letters•Jan 12, 2021•0 citations

Solution of Bloch equations involving amplitude and frequency modulations

F. T. Hioe

The undamped Bloch equations are shown to have a more general analytic solution which includes the famous self-induced-transparency solution of McCall and Hahn, and the nonadiabatic excitation solution of Allen and Eberly as special cases. A generalized area characteristic for a laser pulse of modulated amplitude and frequency of the forms of hyperbolic secant and tangent is given. It resolves the difficulty of the previous area concept in the presence of frequency modulation. The solution provides an exact analytic result for the amplitude- and frequency-modulated pulse of any area.

Physical Review A•Oct 1, 1984•191 citations

Analytic solutions of the optical Bloch equations

Heung‐Ryoul Noh, Wonho Jhe

Optics Communications•Feb 12, 2010•29 citations

Analytic solutions of the Bloch equation involving asymmetric amplitude and frequency modulations

Daniel Rosenfeld, Shimon L. Panfil, Yuval Zur

An analytic solution of the Bloch equation is presented using a class of asymmetric complex functions as a driving function. These may involve both amplitude and frequency modulation functions. Analytic solutions that have been previously derived include the amplitude modulated (``real'') hyperbolic secant pulse and its asymmetric generalization in addition to the complex sech/tanh pulse. The solution presented in this paper contains all of these as particular cases. The solution in its complex form is closely associated with an adiabatic fast passage experiment and renders robust magnetization inversion provided the rf amplitude exceeds a certain threshold. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Sep 1, 1996•21 citations

On the solution of the Bloch equations

E. Arimondo, Davide Bertolini

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Aug 1, 1972•0 citations

Transient solutions of the three-level bloch equations

Christopher Feuillade

Chemical Physics Letters•Aug 1, 1976•10 citations
The undamped Bloch equations are shown to have a more general analytic solution which includes the famous self-induced-transparency solution of McCall and Hahn, and the nonadiabatic excitation solution of Allen and Eberly as special cases. A generalized area characteristic for a laser pulse of modulated amplitude and frequency of the forms of hyperbolic secant and tangent is given. It resolves the difficulty of the previous area concept in the presence of frequency modulation. The solution provides an exact analytic result for the amplitude- and frequency-modulated pulse of any area.
An analytic solution of the Bloch equation is presented using a class of asymmetric complex functions as a driving function. These may involve both amplitude and frequency modulation functions. Analytic solutions that have been previously derived include the amplitude modulated (``real'') hyperbolic secant pulse and its asymmetric generalization in addition to the complex sech/tanh pulse. The solution presented in this paper contains all of these as particular cases. The solution in its complex form is closely associated with an adiabatic fast passage experiment and renders robust magnetization inversion provided the rf amplitude exceeds a certain threshold. \textcopyright{} 1996 The American Physical Society.